Simplify to lowest terms. $\dfrac{24}{80}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 24 and 80? $24 = 2\cdot2\cdot2\cdot3$ $80 = 2\cdot2\cdot2\cdot2\cdot5$ $\mbox{GCD}(24, 80) = 2\cdot2\cdot2 = 8$ $\dfrac{24}{80} = \dfrac{3 \cdot 8}{ 10\cdot 8}$ $\hphantom{\dfrac{24}{80}} = \dfrac{3}{10} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{24}{80}} = \dfrac{3}{10} \cdot 1$ $\hphantom{\dfrac{24}{80}} = \dfrac{3}{10}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{24}{80}= \dfrac{2\cdot12}{2\cdot40}= \dfrac{2\cdot 2\cdot6}{2\cdot 2\cdot20}= \dfrac{2\cdot 2\cdot 2\cdot3}{2\cdot 2\cdot 2\cdot10}= \dfrac{3}{10}$